Question 12.2: Flat-screen TV Sales Study Refer to the management scenario ......
Flat-screen TV Sales Study
Refer to the management scenario of Example 12.1. Find the sample correlation coefficient, r, between the number of ads placed and flat-screen TV sales. Comment on the strength of the linear relationship.
Step-by-Step
Table 12.4 shows the calculations for Pearson’s sample correlation coefficient, r.
Table 12.4 gives \sum{x}=44,\ \sum{y=346,\ \sum{x^2} }=174,\ \sum{xy}=1324,\ \sum{y^2}=10336\ \text{and}\ n=12.
Then: r = \frac{12(1324)-(44)(346)}{\sqrt{[12(174)-(44)^2][12(10336)-(346)^2]} }=\frac{664}{\sqrt{(152)(4316)} }
= 0.8198 (Formula 12.5)
Table 12.4 Pearson’s correlation coefficient for the flat-screen TV sales study
| Ads (x) | Sales (y) | x^2 | xy | y^2 |
| 4 | 26 | 16 | 104 | 676 |
| 4 | 28 | 16 | 112 | 784 |
| 3 | 24 | 9 | 72 | 576 |
| 2 | 18 | 4 | 36 | 324 |
| 5 | 35 | 25 | 175 | 1225 |
| 2 | 24 | 4 | 48 | 576 |
| 4 | 36 | 14 | 144 | 1296 |
| 3 | 25 | 9 | 75 | 625 |
| 5 | 31 | 25 | 155 | 961 |
| 5 | 37 | 25 | 185 | 1369 |
| 3 | 30 | 9 | 90 | 900 |
| 4 | 32 | 16 | 128 | 1024 |
| 44 | 346 | 174 | 1324 | 10336 |
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